Mathematical procedures that promise an envy-free, equitable, and efficient solution to distributional conflicts have received widespread attention. Two fair-division mechanisms, adjusted Knaster and proportional Knaster, which are similar to the well-known adjusted-winner procedure, are compared with the less fair divide-and-choose mechanism. Results show that participants largely prefer the adjusted-Knaster procedure to the two alternatives. Adjusted Knaster, closely followed by proportional Knaster, also promises the highest average payoff. Yet the sophisticated mechanisms cease to perform better than divide-and-choose once actors receive the possibility to deviate from the mandatory bargaining protocols of fair-division procedures. The preference for adjusted and proportional Knaster is found to be a partial function of the participants psychological profile. The more antisocial a participant, the more likely this respondent is to opt for a procedure with a compensatory mechanism.